Scheduling jobs on parallel machines: a restricted tabu search approach

Many real scheduling problems are often much more complex than problems that are analytically tractable. The main difficulty in obtaining optimal job schedules arises from the existence of sequence dependent setup times among jobs and job release times. In this paper, we present a restricted tabu search algorithm that schedules jobs on parallel machines in order to minimise the maximum lateness of the jobs. The jobs have release times and due dates, and sequence-dependent setup times exist between the jobs. The parallel machines are either identical or non-identical in terms of the processing times of the jobs. The restricted tabu search algorithm employs a restricted search with the elimination of non-effective job moves, for finding the best neighbourhood schedule. The restricted search algorithm reduces search effort significantly while obtaining good quality final schedule. The experimental results show that the proposed algorithm obtains much better solutions more quickly than other heuristic algorithms such as the Rolling Horizon Procedure (RHP) heuristic, the basic tabu search and simulated annealing.     

Iterated hybrid metaheuristic algorithms for unrelated parallel machines problem with unequal ready times and sequence-dependent setup times

The problem considered in this paper involves a set of independent jobs on unrelated parallel machines with sequence-dependent setup times and unequal ready times, and the objective is to minimize the weighted number of tardy jobs. Iterated hybrid metaheuristic algorithms are proposed to address this problem. The algorithms begin with effective initial solution generators to generate initial feasible solutions; then, hybrid metaheuristics are applied to improve the initial solutions, integrating the principles of the variable neighborhood descent approach and tabu search. If the search becomes trapped at a local optimum, a perturbation operator is developed to help the search escape. To evaluate the performance of the suggested algorithms, heuristic rules and iterated local search algorithms are examined and compared. Computational experimental results show that the proposed algorithms outperform the other heuristics.     

Meta-heuristics to solve single-machine scheduling problem with sequence-dependent setup time and deteriorating jobs

This paper tackles the single-machine scheduling problem in which there are sequence-dependent setup times and deteriorating jobs. In this regard, a mathematical model has been formulated to minimize makespan (C _max). Afterwards, genetic and tabu search algorithms have been developed. Since the population diversity is a very important issue in preventing neighborhood search from trapping in a local optimum, some methods have been applied to genetic algorithm in order to maintain population diversity, and the final results show the effectiveness of these methods. The calibration of genetic algorithm parameters and operators is performed using design of experiments. Finally, several examples are produced to illustrate the proposed approach.     

An ant colony algorithm for scheduling in flowshops with sequence-dependent setup times of jobs

The problem of scheduling in flowshops with sequence-dependent setup times of jobs is considered and solved by making use of ant colony optimization (ACO) algorithms. ACO is an algorithmic approach, inspired by the foraging behavior of real ants, that can be applied to the solution of combinatorial optimization problems. A new ant colony algorithm has been developed in this paper to solve the flowshop scheduling problem with the consideration of sequence-dependent setup times of jobs. The objective is to minimize the makespan. Artificial ants are used to construct solutions for flowshop scheduling problems, and the solutions are subsequently improved by a local search procedure. An existing ant colony algorithm and the proposed ant colony algorithm were compared with two existing heuristics. It was found after extensive computational investigation that the proposed ant colony algorithm gives promising and better results, as compared to those solutions given by the existing ant colony algorithm and the existing heuristics, for the flowshop scheduling problem under study.     

Hybrid metaheuristics for unrelated parallel machine scheduling with sequence-dependent setup times

This paper proposes several hybrid metaheuristics for the unrelated parallel-machine scheduling problem with sequence-dependent setup times given the objective of minimizing the weighted number of tardy jobs. The metaheuristics begin with effective initial solution generators to generate initial feasible solutions; then, they improve the initial solutions by an approach, which integrates the principles of the variable neighborhood descent approach and tabu search. Four reduced-size neighborhood structures and two search strategies are proposed in the metaheuristics to enhance their effectiveness and efficiency. Five factors are used to design 32 experimental conditions, and ten test problems are generated for each condition. Computational results show that the proposed hybrid metaheuristics are significantly superior to several basic tabu search heuristics under all the experimental conditions.     

调整时间与顺序相关的等同并行机调度

调整时间与顺序相关的等同并行机调度在生产服务业与制造业中有着十分广泛的应用背景,具有计算复杂性的主要特点。调整时间与顺序相关的等同并行机调度是将被加工工件集的各工件分配给等同并行机资源,并安排工件的加工次序。它是决策的一种形式,其目的是优化一个或多个目标。研究以最小化被加工工件最大完工时间为目标的调整时间与顺序相关的等同并行机调度,建立该问题的数学规划模型,根据问题的结构特点开发基于两段式染色体表达的遗传算法以获得该问题的近似最优解;在所建立数学规划模型的基础上,引入所求解问题的下界对近似最优解的质量进行评价。对具有不同规模的问题实例进行计算试验,计算结果表明所设计的遗传算法能够在可接受的计算时间内获得合理的解。     

A novel hybrid genetic algorithm to solve the sequence-dependent permutation flow-shop scheduling problem

Flow-shop scheduling problem (FSP) deals with the scheduling of a set of jobs that visit a set of machines in the same order. The FSP is NP-hard, which means that there is no efficient algorithm to reach the optimal solution of the problem. To minimize the make-span of large permutation flow-shop scheduling problems in which there are sequence-dependent setup times on each machine, this paper develops one novel hybrid genetic algorithms (HGA). Proposed HGA apply a modified approach to generate the population of initial chromosomes and also use an improved heuristic called the iterated swap procedure to improve them. Also the author uses three genetic operators to make good new offspring. The results are compared to some recently developed heuristics and computational experimental results show that the proposed HGA performs very competitively with respect to accuracy and efficiency of the solutions.     

A Tabu Search Algorithm for Single Machine Scheduling with Release Times,Due Dates,and Sequence-Dependent Set-up Times

In this paper, we present a tabu search algorithm that schedules N jobs to a single machine in order to minimise the maximum lateness of the jobs. The release times, due dates, and sequence-dependent set-up times of the jobs are assumed to exist. We modified the original tabu search method to be suitable for the scheduling problem. The proposed tabu search algorithm is composed of two parts: a MATCS (modified apparent tardiness cost with set-ups) rule for finding an efficient initial solution, and the tabu search method to seek a near optimal solution from the initial solution. The experimental results show that the tabu search algorithm obtains much better solutions more quickly than the RHP (rolling horizon procedure) heuristic suggested by Ovacik and Uzsoy.     

Scheduling on unrelated parallel machines with sequence- and machine-dependent setup times and due-date constraints

We consider the unrelated parallel-machine scheduling problem with sequence- and machine-dependent setup times and due-date constraints. There are N jobs, each having a due date and requiring a single operation on one of the M machines. A setup is required if there is a switch from processing one type of job to another. Due to the characteristics of machines, the processing time depends upon the job and machine on which the job is processed, and the setup time is sequence and machine dependent. In addition, certain jobs have strict due-date constraints. An effective heuristic based on a modified apparent-tardiness-cost-with-setup procedure, the simulated annealing method, and designed improvement procedures is proposed to minimize the total tardiness of this scheduling problem. Computational characteristics of the proposed heuristic are evaluated through an extensive experiment using a newly created data set. Computational results show that the proposed heuristic is able to effectively improve the initial solutions, obtained by a modified apparent-tardiness-cost-with-setup procedure, and obtains better results than a random descent heuristic.     

An improved iterated greedy algorithm for the no-wait flow shop scheduling problem with makespan criterion

An improved iterated greedy algorithm (IIGA) is proposed in this paper to solve the no-wait flow shop scheduling problem with the objective to minimize the makespan. In the proposed IIGA, firstly, a speed-up method for the insert neighborhood is developed to evaluate the whole insert neighborhood of a single solution with (n???1)² neighbors in time O(n ²), where n is the number of jobs; secondly, an improved Nawaz-Enscore-Ham (NEH) heuristic is presented for constructing solutions in the initial stage and searching process; thirdly, a simple local search algorithm based on the speed-up method is incorporated into the iterated greedy algorithm to perform exploitation. The computational results based on some well-known benchmarks show that the proposed IIGA can obtain results better than those from some existing approaches in the literature.     

Minimization of maximum tardiness on unrelated parallel machines with process restrictions and setups

We consider the problem of scheduling N jobs on M unrelated parallel machines to minimize maximum tardiness. Each job has a due date and requires a single stage of processing. A setup for dies is incurred if the type of the job scheduled is different from the previous one on that machine. For each die type, the number of dies is restricted. Because of the mechanical structure of the machines and the fitness of dies to each machine, the processing time depends on both the job and the machine. In this paper, an efficient heuristic based on guided search, record-to-record travel, and tabu lists is presented to minimize maximum tardiness. Computational characteristics of the proposed heuristic are evaluated through extensive experiments, which show that the proposed heuristic outperforms a simulated annealing method tested and is able to prescribe the optimal solutions for problems in small scales.     

Scheduling jobs on dynamic parallel machines with sequence-dependent setup times

Dynamic parallel machine scheduling problems (DPMSPs) with sequence-dependent setup times represent a very important production scheduling problem but remain under-represented in the research literature. In this study, a restricted simulated annealing (RSA) algorithm that incorporates a restricted search strategy with the elimination of non-effect job moves to find the best neighborhood schedule is presented. The proposed RSA algorithm can reduce search efforts significantly while minimizing maximum lateness on DPMSPs. Extensive computational experiments demonstrate that the proposed RSA algorithm is highly effective as compared to the basic simulated annealing and existing algorithms on the same benchmark problem data set.     

Minimization of maximum tardiness on unrelated parallel machines with process restrictions and setups

We consider the problem of schedulingN jobs onM unrelated parallel machines to minimize maximum tardiness. Each job has a due date and requires a single stage of processing. A setup for dies is incurred if the type of the job scheduled is different from the previous one on that machine. For each die type, the number of dies is restricted. Because of the mechanical structure of the machines and the fitness of dies to each machine, the processing time depends on both the job and the machine. In this paper, an efficient heuristic based on guided search, record-to-record travel, and tabu lists is presented to minimize maximum tardiness. Computational characteristics of the proposed heuristic are evaluated through extensive experiments, which show that the proposed heuristic outperforms a simulated annealing method tested and is able to prescribe the optimal solutions for problems in small scales.     

Solving single-machine total weighted tardiness problems with sequence-dependent setup times by meta-heuristics

Simulated annealing (SA), genetic algorithms (GA), and tabu search (TS) are the three well known meta-heuristics for combinatorial optimization problems. In this paper, single-machine total weighted tardiness problems with sequence-dependent setup times are solved by SA, GA, and TS approaches. A random swap and insertion search is applied in SA, and a mutation operator performed by a greedy local search is used in a GA. Similarly, a swap and an insertion tabu list are adopted in TS. To verify these proposed approaches, computational experiments were conducted on benchmark problem sets. The experimental results show that these approaches find new upper bound values for most benchmark problems within reasonable computational expenses.     

A due date density-based categorising heuristic for parallel machines scheduling

The effective management of shop floor resources is an important factor in achieving the goals of a manufacturing company. The need for effective scheduling is particularly strong in complex manufacturing environments. This paper presents an efficient due date density-based categorising heuristic to minimise the total weighted tardiness (TWT) of a set of tasks with known processing times, due dates, weights and sequence-dependent setup times for parallel machines scheduling. The proposed heuristic is composed of four phases. In the first phase, jobs are listed by the earliest due date (EDD). The second phase computes the due date gaps between listed jobs and categorises the jobs based on the due date density. In the third phase, the sequence of jobs is improved by a tabu search (TS) method. The fourth phase allocates each job to machines. The comprehensive simulation results show that the proposed heuristic performs better than other existing heuristics at a significantly reduced total weighted tardiness.     

An intelligent hybrid meta-heuristic for solving a case of no-wait two-stage flexible flow shop scheduling problem with unrelated parallel machines

This paper addresses the problem of no-wait two-stage flexible flow shop scheduling problem (NWTSFFSSP) considering unrelated parallel machines, sequence-dependent setup times, probable reworks and different ready times to actualize the problem. The performance measure used in this study is minimizing maximum completion time (makespan). Because of the complexity of addressed problem, we propose a novel intelligent hybrid algorithm [called hybrid algorithm (HA)] based on imperialist competitive algorithm (ICA) which are combined with simulated annealing (SA), variable neighborhood search (VNS) and genetic algorithm (GA) for solving the mentioned problem. The hybridization is carried out to overcome some existing drawbacks of each of these three algorithms and also for increasing the capability of ICA. To achieve reliable results, Taguchi approach is used to define robust parameters' values for our proposed algorithm. A simulation model is developed to study the performance of our proposed algorithm against ICA, SA, VNS, GA and ant colony optimization (ACO). The results of the study reveal the relative superiority of HA studied. In addition, potential areas for further researches are highlighted.     

Development and analysis of constructive heuristic algorithms for flow shop scheduling problems with sequence-dependent setup times

This paper focuses on the problem of determining a permutation schedule for n jobs in an m-machine flow shop that operates in a sequence-dependent setup time (SDST) environment. Two constructive heuristic algorithms are developed with the minimisation of makespan as the objective. The first heuristic algorithm termed as setup ranking algorithm obtains the sequence using the setup times of jobs only. The second heuristic algorithm, fictitious job setup ranking algorithm (FJSRA), is developed using the concept of fictitious jobs. Pairs of jobs with minimum setup time between them constitute the fictitious jobs. Both these algorithms are compared with an existing constructive algorithm. For the purpose of experimentation, Taillard benchmark problems are used to develop SDST benchmark problems at eight different levels of sequence-dependent setup times. Graphical analysis, relative performance index analysis and statistical analysis are carried out on the results obtained for all the eight sets of benchmark problems. The analysis reveals that FJSRA emerges as the better algorithm for larger problems and for smaller problems with higher level of setup time. The results of statistical analysis are used to develop setup time dominance matrix for deciding upon the algorithm to be used for a particular size of problem.     

Minimization of total tardiness on unrelated parallel machines with sequence- and machine-dependent setup times under due date constraints

The unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times in the presence of due date constraints represents an important but relatively less-studied scheduling problem in the literature. In this study, a simple iterated greedy (IG) heuristic is presented to minimize the total tardiness of this scheduling problem. The effectiveness and efficiency of the proposed IG heuristic are compared with existing algorithms on a benchmark problem dataset used in earlier studies. Extensive computational results indicate that the proposed IG heuristic is capable of obtaining significantly better solutions than the state-of-the-art algorithms on the same benchmark problem dataset with similar computational resources.     

An improved hybrid multi-objective parallel genetic algorithm for hybrid flow shop scheduling with unrelated parallel machines

In this paper, we address the hybrid flow shop scheduling problems with unrelated parallel machines, sequence-dependent setup times and processor blocking to minimize the makespan and maximum tardiness criteria. Since the problem is strongly NP-hard, we propose an effective algorithm consisting of independent parallel genetic algorithms by dividing the whole population into multiple subpopulations. Each subpopulation will be assigned with different weights to search for optimal solutions in different directions. To further cover the Pareto solutions, each algorithm is combined with a novel local search step and a new helpful procedure called Redirect. The proposed Redirect procedure tries to help the algorithm to overcome the local optimums and to further search the solution space. When a population stalls over a local optimum, at first, the algorithm tries to achieve a better solution by implementing the local search step based on elite chromosomes. As implementing the local search step is time-consuming, we propose a method to speed up the searching procedure and to further increase its efficiency. If the local search step failed to work, then the Redirect procedure changes the direction and refreshes the population. Computational experiments indicate that our proposed improving procedures are thriving in achieving better solutions. We have chosen two measures to evaluate the performance of our proposed algorithms. The obtained results clearly reveal the prosperity of our proposed algorithm considering both measures we have chosen.     

Due windows group scheduling using an effective hybrid optimization approach

This paper considers the problem of scheduling part families (groups) and jobs within each part family in a hybrid flow shop manufacturing cell with sequence-dependent family setups times where jobs should be completed at times as close as possible to their respective due dates, and hence both earliness and tardiness should be penalized while processing parts (jobs) in each family together. It is assumed that earliness and tardiness penalties will not occur if a job is completed within the due window. The objective is to determine a schedule that minimizes sum of the earliness and tardiness of jobs. To this problem, the hybrid metaheuristic algorithm combined elements from particle swarm optimization; simulated annealing and variable neighborhood search are developed. The aim of using a hybrid metaheuristic is to raise the level of generality so as to be able to apply the same solution method to several problems. Problem sizes ranging in size from small, medium, to large are considered along with three levels of flexibility. The higher the number of stages and the number of parallel machines in each stage, the higher is the flexibility introduced into the problem. A design of experiments approach is employed to calibrate the parameters and operators of the algorithm. We present computational experiments on 126 problems and compare the results with the simulated annealing and genetic algorithms that presented recently. The computational results show that our proposed algorithm is more efficient than the other methods.